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Hybridization between genetically distinct taxa is a complex evolutionary process. One challenge to studying hybrid populations is quantifying the degree to which non-native genes have become evenly mixed among individuals in the population. In this paper, we present a variance-based parameter, md, that measures the degree to which non-native genes are evenly distributed among individuals in a population. The parameter has a minimum value of 0 for populations in which individuals from multiple taxa are present but have not interbred, and a maximum value of 1 for populations in which all individuals have the same amount of non-native ancestry. A recurrence equation showed that relatively few generations of random mating are required for md to approach 1 (indicating a well-mixed population), and that md is independent of initial amounts of non-native ancestry. The parameter is mathematically equivalent to FST and we show how existing formulae for FST can be used to estimate md when diagnostic loci are available. Computer simulations showed this estimator to have very little bias for realistic amounts of data.

One of the primary goals of population genetics is to succinctly describe genetic relationships among populations, and the computer program STRUCTURE is one of the most frequently used tools for doing so. The mathematical model used by STRUCTURE was designed to sort individuals into Hardy-Weinberg populations, but the program is also frequently used to group individuals from a large number of populations into a small number of clusters that are supposed to represent the main genetic divisions within species. In this study, I used computer simulations to examine how well STRUCTURE accomplishes this latter task. Simulations of populations that had a simple hierarchical history of fragmentation showed that when there were relatively long divergence times within evolutionary lineages, the clusters created by STRUCTURE were frequently not consistent with the evolutionary history of the populations. These difficulties can be attributed to forcing STRUCTURE to place individuals into too few clusters. Simulations also showed that the clusters produced by STRUCTURE can be strongly influenced by variation in sample size. In some circumstances, STRUCTURE simply put all of the individuals from the largest sample in the same cluster. A reanalysis of human population structure suggests that the problems I identified with STRUCTURE in simulations may have obscured relationships among human populations-particularly genetic similarity between Europeans and some African populations.

Bifurcating evolutionary trees are commonly used to describe genetic relationships between populations, but may not be appropriate for populations that did not evolve in a hierarchical manner. The degree to which bifurcating trees distort genetic relationships between populations can be quantified with R(2), the proportion the variation in a matrix of genetic distances between populations that is explained by a tree. Computer simulations were used to measure how well the unweighted pair group method with arithmetic mean (UPGMA) and neighbor-joining (NJ) trees depicted population structure for three evolutionary models: a hierarchical model of population fragmentation, a linear stepping-stone model of gene flow and a two-dimensional stepping-stone model of gene flow. These simulations showed that the UPGMA did an excellent job of describing population structure when populations had a bifurcating history of fragmentation, but severely distorted genetic relationships for the linear and two-dimensional stepping-stone models. The NJ algorithm worked well in a broader range of evolutionary histories, including the linear stepping-stone model. A computer program for performing the calculations described in this study is available for download at www.montana.edu/kalinowski.

Relatedness is often estimated from microsatellite genotypes that include null alleles. When null alleles are present, observed genotypes represent one of several possible true genotypes. If null alleles are detected, but analyses do not adjust for their presence (ie, observed genotypes are treated as true genotypes), then estimates of relatedness and relationship can be incorrect. The number of loci available in many wildlife studies is limited, and loci with null alleles are commonly a large proportion of data that cannot be discarded without substantial loss of power. To resolve this problem, we present a new approach for estimating relatedness and relationships from data sets that include null alleles. Once it is recognized that the probability of the observed genotypes is dependent on the probabilities of a limited number of possible true genotypes, the required adjustments are straightforward. The concept can be applied to any existing estimators of relatedness and relationships. We review established maximum likelihood estimators and apply the correction in that setting. In an application of the corrected method to data from striped hyenas, we demonstrate that correcting for the presence of null alleles affect results substantially. Finally, we use simulated data to confirm that this method works better than two common approaches, namely ignoring the presence of null alleles or discarding affected loci.

The coefficient of variation of estimates of three genetic distances (standard genetic distance of Nei, chord distance, FST) was examined with computer simulation to determine if large samples (per population) are necessary to precisely estimate genetic distances at loci with high levels of polymorphism. These simulations showed that loci with high mutation rates produce estimates of genetic distance with lower coefficients of variation than loci with lower mutation rates--without requiring larger sample sizes from each population. In addition, the rate at which increasing sample sizes decreases the coefficient of variation of estimates of genetic distances was shown to be approximately determined by the value of FST between the populations being sampled. When FST was greater than 0.05, sampling fewer than 20 individuals (per population) should be sufficient. When FST was less than 0.01, sampling 100 individuals (per population) or more will be useful.

As more microsatellite loci become available for use in genetic surveys of population structure, population geneticists are able to select loci to use in population structure surveys. This study used computer simulations to investigate how the number of alleles at loci affects the precision of estimates of four common genetic distances. This showed that equivalent results could be achieved by examining either a few loci with many alleles or many loci with a few alleles. More specifically, the total number of independent alleles appears to be a good indicator of how precise estimates of genetic distance will be.

The great expansion of population genetic data using molecular techniques now allows examination of the extent of linkage disequilibrium for many pairs of loci, each locus often with multiple alleles. The expectation-maximization (EM) algorithm for generating maximum likelihood estimates of gametic frequencies from multiallelic genotypic data is described and applied. The EM algorithm is used in desert bighorn sheep where the population size, and consequently the sample size, is often small. We calculated haplotype frequencies for all pairwise combinations of five major histocompatibility loci and three microsatellite loci in 14 populations; the performance of the algorithm is discussed. Disequilibrium values are calculated and tested for statistical significance. High levels of disequilibrium are found between all pairs of major histocompatibility complex (MHC) loci and between MHC and a linked microsatellite locus.

Bighorn sheep populations have greatly declined in numbers and distribution since European settlement, primarily because of high susceptibility to infectious diseases transmitted to them from domestic livestock. It has been suggested that low variation at major histocompatibility complex (MHC) genes, the most important genetic aspect of the vertebrate immune system, may result in high susceptibility to infectious disease. Therefore, we examined genetic polymorphism at a MHC gene (Ovca-DRB) in a large sample, both numerically and geographically, of bighorn sheep. Strikingly, there were 21 different alleles that showed extensive nucleotide and amino acid sequence divergence. In other words, low MHC variation does not appear to be the basis of the high disease susceptibility and decline in bighorn sheep. On the other hand, analysis of the pattern of the MHC polymorphism suggested that nonsynonymous substitutions predominated, especially at amino acids in the antigen-binding site. The average overall heterozygosity for the 16 amino acid positions that are part of the antigen binding site is 0.389 whereas that for the 67 amino acid positions not involved with antigen binding is 0.076. These findings imply that the diversity present in this gene is functionally significant and is, or has been, maintained by balancing selection. To examine the evolution of DRB alleles in related species, a phylogenetic analysis including other published ruminant (Bovidae and Cervidae) species, was carried out. An intermixture of sequences from bighorn sheep, domestic sheep, goats, cattle, bison, and musk ox was observed supporting trans-species polymorphism for these species. To reconcile the species and gene trees for the 104 sequences examined, 95 'deep coalescent' events were necessary, illustrating the importance of balancing selection maintaining variation over speciation events.

During the screening of the natural products for their ability to increase the activity of glucokinase by relieving inhibition by long chain fatty acyl CoA esters (FAC), two novel compounds, glucolipsin A (1) and B (2) were isolated from the butanol extracts of Streptomyces purpurogeniscleroticus WC71634 and Nocardia vaccinii WC65712, respectively. The structures of these two compounds were established by spectroscopic methods and chemical degradation. Glucolipsin A (1) and B (2) relieved the inhibition of glucokinase by FAC with RC50 values of 5.4 and 4.6 microM.